What is the answer to (x+iy)/(1+x+iy)=3+4i ?

The answer to (x+iy)/(1+x+iy)=3+4i is x=-11/10 ,y= 1/5

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(x+iy)/(1+x+iy)=3+4i

\frac{x + i y}{1 + x + i y} = 3 + 4 i

x = - \frac{11}{10}, y = \frac{1}{5}

Solution steps

\frac{x + i y}{1 + x + i y} = 3 + 4 i

Multiply both sides by

1 + x + i y

\frac{x + i y}{1 + x + i y} (1 + x + i y) = 3 (1 + x + i y) + 4 i (1 + x + i y)

Expand

x + i y = (3 + 3 x - 4 y) + i (4 + 3 y + 4 x)

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[x = 3 + 3 x - 4 y y = 4 + 3 y + 4 x]

[x = 3 + 3 x - 4 y y = 4 + 3 y + 4 x] : x = - \frac{11}{10}, y = \frac{1}{5}

x = - \frac{11}{10}, y = \frac{1}{5}

4 (3 i + 2) - 2 i = (2 x) i + y

3 x - 2 y i = 6 + 4 i

p (2 i + 6 j) + q (2 i - 4 j) = 6 i - 7 j

(3 + i) x^{2} + 10 x - (9 + 3 i) = 0

z^{2} + i z + (1 - i) = 0

What is the answer to (x+iy)/(1+x+iy)=3+4i ?
The answer to (x+iy)/(1+x+iy)=3+4i is x=-11/10 ,y= 1/5